Beat the eggs in a mixing bowl. Whisk in the milk, then set aside. Place the bread crumbs into a plastic bag, and set aside.
Separate and place an egg roll wrapper onto your work surface with one of the tips pointed towards you. Moisten the two far edges of the wrapper with water. Place a string cheese stick onto the corner nearest you, and roll it in 1/3 of the way, fold over the right and left corners, then continue rolling to the end, pressing to seal. Repeat with the remaining string cheese sticks and egg roll wrappers.
Heat oil in a deep-fryer or large saucepan to 375 degrees F (190 degrees C).
Dip the mozzarella sticks into the egg wash, then toss in the bread crumbs. Cook in batches in the hot oil until crisp and golden brown, 3 to 4 minutes.